We present the spine calculus S-> -o&T as an
efficient representation for the linear lambda-calculus
lambda -> -o&T which includes intuitionistic functions
(->), linear functions - o , additive pairing (&), and additive
unit T. S-> -o&T enhances the representation of Church's
simply typed lambda-calculus as abstract Bohm trees by enforcing extensionality
and by incorporating linear constructs. This approach permits procedures
such as unification to retain the efficient head access that characterizes
first-order term languages without the overhead of performing
n-conversions at run time. Potential applications lie in proof search,
logic programming, and logical frameworks based on linear type theories. We
define the spine calculus, give translations of lambda -> -o&T
into S -> -o&T and vice-versa, prove their soundness
and completeness with respect to typing and reductions, and show that the
spine calculus is strongly normalizing and admits unique canonical forms.
36 pages